the first lesson
Game elements:
- participant
- Strategy selection (policy set)
- Strategy combination
- income
This is the first official contact with the game theory
strategy is defined as a written form: behavior affect the outcome, however, depends not only on the results of your actions, and also depends on the behavior of others.
Textbook
Dutta's "strategy and game", Joel Watson's "strategy" there is another one "strategic thinking"
The first game
Prisoner's Dilemma 
majority of students choose to live α, β small selection of
game theory can help us to choose life goals, can only help us reach the goal. In other words, the goal of life is to rely on our own inner knowledge and vision size
is defined:
If you choose to α stringent than the results obtained β, then β is a relatively strictly dominant strategy, the focus is: no matter what they choose, do not choose strictly dominated strategy
why?
Studies on A: Because everyone will choose the dominant strategy, which led to worse results, the overall results worse
Student B: "You'll never win,"
Student C: lower earnings.
Concorde fallacy 
demon eater and angry angel game
assume that we are the devil eater: 
Here I chose α, because for us is the dominant strategy.
Suppose the contrary, we are angry angel: 
For us choose not superior to α β, but we chose α, α choice because it is for the other dominant strategy, so the other party will choose a high probability α.
Conclusion: The best way to analyze the game, which is the core strategy analysis are: empathy
Social Survey:
70% Select alpha
30% opted β
Student A: Select the β will average increase.
Student B: long-term election Game β, the benefits outweigh the α.
第二个游戏
ex，total = 5
5， 25， 60
ave = 30
win = 25
money = 5-0.05=4.95
多个玩家胜利，大家平分奖金
第一节课的五个结论
- 不要选择劣势策略
- 耶鲁大学的学生很自私
- 理性选择导致次优的结果
- 你无法得到想要的
- 学会换位思考
博弈论于现实世界是紧密联系的
- 囚徒博弈
- 集体作业（大家都想偷懒）
- 企业价格战
- 共同的资源（碳排放、公海捕鱼、）
跳出思维定势：制定协议（改变收益）
博弈的要素
组成：
- 参与人
- 策略集合
- 收益
游戏1
收益分配为
这里的I和II都没有优势策略
游戏2
大多数学生选择防守平坦的路
但是这个并不是一个合理的答案。
学生原因：人为中心地认为侵略者会选择平坦的那条路，以维持士兵数量的最大化。
我们要从对面的角度进行思考，对于侵略者（汉尼拔）而言
弱优于：它意味着选择平坦之途较选择崎岖之途而言至少要同样的好，可能还稍微好些
回归上期的数学游戏
大概有9个人选择了32,33,34。
有一个人选择了30，原因是
而大家会选笔比那小的，所以他就选择了一个更小的。
老师解释选择33的原因是，如果大家在【1,100】中随机选择，平均数会是50左右，50的2/3就是33.
然而学生并不会随机选择，所以最终数字会比33小，然后大概有12个人选择了22，因为33的2/3==22
.
选择直接剔除策略：“没有人会选择大于50的数”
如果每个人都选择100的话，最后的数为67，但是实时上不会，所以直接剔除掉67-100的数字。得出“没人会选择67以上的数”可以推出下一个结论“大于45的数会被剔除”。
意识到别人不会选择劣势策略之后，我们本身也不应该选择劣势策略。
Then eliminate disadvantages strategy, which is then × 2/3, then the number of stars 30 and 45 are also removed, then ....
: I know one thing, you know it, you know I know it, I know you know this, and so an infinite loop.
Finally, the optimal strategy is to 1, and most of the students chose 1, the final result is 9. (average of 13 and 1 / 3,2 / 3 to 9) nine individuals selected 9
The end result of this game is declining.
Finally, we emphasize common knowledge: let the two came, respectively, to two a hat. They know each other color hat, but do not know the color of his own hat, so even though they know at least one person with a pink hat, this is mutual knowledge. Mutual knowledge is not public knowledge.
Common knowledge does not just know what I'm hungry, and I know if people know I know people know. . . . And so on